1. Field of the Invention
The present invention relates to a computer generated hologram display technique for obtaining interferences between a wavefront of light from an object and a wavefront of a reference light by calculations, and displaying the resulting interference fringes as a hologram representing a three-dimensional image.
2. Description of the Background Art
The conventionally known methods for producing computer generated holograms include a method using FFT (Fast Fourier Transform) (see W. H. Lee, "Sampled Fourier Transform Hologram Generated by Computer", Applied Optics, Vol. 9, No. 3, pp. 639-643, 1970, for example) and a method in which an object is described as a set of point objects and wavefronts of lights from the point objects are synthesized (see J. P. Waters, "Holographic Image Synthesis Utilizing Theoretical Methods", Applied Physics Letters, Vol. 9, No. 11, 1966, for example).
The former method has an advantage in that the computation can be carried out at relatively high speed for a discretized flat plane object, but it presupposes the use of a flat plane object as its processing target so that a three-dimensional object must be displayed as a set of plural cross-sections. For this reason, the advantage due to the high speed characteristic of the FFT becomes less significant as a required number of cross-sections increases, and the computation can be rather slow when a display target space is to be enlarged or a resolution is to be raised. On the other hand, the latter method requires a longer computation time because of the description using point objects, but it is unaffected by the size or the resolution of the display target space so that it is suitable for producing holograms in high resolution and wide viewfield.
In the method for describing an object by a set of point objects, these point objects are regarded as point light sources, and a wavefront of light reflected from the object is calculated by synthesizing wavefronts of lights generated from these point light sources. Namely, in an exemplary coordinate system for calculating computer generated holograms, the orthogonal coordinates with an origin on a hologram plane is defined and a position of a point light source is defined as P(x.sub..0., y.sub..0., z.sub..0.). Then, when the reference light is assumed to be a plane wave R. the wavefronts of light from the point light source P and the reference light can be expressed in terms of complex amplitudes as follows. EQU P=(a/r)e.sup.jkr, R=Ae.sup.jkr (1)
In the computational holography, these two wavefronts are synthesized and a hologram is obtained by the calculating the following quantity. EQU .vertline.P+R.vertline..sup.2 (2)
However, in the latter method, the holographic video display has been realized by calculating in advance all the frames to be presented, storing the calculated results in a storage device such as real time disk device, and reading the stored data at high speed.
There are also some attempts for high speed real time calculation of the interference fringes using a super-computer and the like (see M. Lucente and T. A. Galyean, "Rendering Interactive Holographic Images", Computer Graphics (SIGGRAPH'95), pp. 387-394, 1995, for example), but these attempts basically adopt a scheme in which each frame is to be calculated independently, so that the resolution and the size of a display image that can actually be computed have been limited.
There is also a proposition for reducing an amount of hologram calculations by utilizing difference data of display images (see, H. Takahashi, et al., "Direct volume access by an improved electro-holography image generator" SPIE, Vol. 2406, pp. 220-225, 1995), but this proposition only decomposes a display target object into a plurality of parts and carries out addition or subtraction of interference fringes for each part, so that this proposition cannot realize an effective reduction of an amount of calculations for the video display.
Thus, in the production of interference fringes in real time by a computer, the following problems are encountered in practice.
(1) An amount of calculations required by a scheme for calculating each frame independently is so large that, at present, the video production is impossible unless a super- computer is employed.
(2) In the scheme for calculating each frame independently, when an area of the hologram is increased or a number of objects is increased beyond some limit, it becomes impossible to realize the real time calculation even by massively parallel processing machines, so that there is a limit to the video display using a scheme for producing interference fringes for each frame independently.
Now, in the production of computer generated holograms, there is a need to display interference fringes at high resolution in order to cause the diffraction of light. To this end, it is necessary to process an enormous number of pixels far greater than those processed in a conventional high precision display device such as HDTV, even when a display screen is small. Also, in the interference fringe calculations, a value obtained by synthesizing the wavefronts of lights from the entire display target object is going to be a value at each point (pixel) of the interference fringes, so that the major problem to be resolved is an increase in an amount of calculations due to an increase in a number of pixels to be displayed.
One way of resolving this problem is a method which provides the high resolution display only at a gaze point based on a gaze detection, which is a two-dimensional large screen display method. This method follows a line of gaze and displays only objects on the line of gaze at high resolution, so as to reduce an amount of calculations required for producing images to be displayed and to enable a large screen display at the same time.
On the other hand, in the binocular disparity display device such as HMD, there is a proposition in which lines of gaze for left and right eyes are detected and a gaze point (focal length) of an observer is detected from the intersection of the detected lines of gaze, and then objects in a gazed region are displayed in focus (see S. Shiwa et al., "Proposal for a 3-D display with accommodative compensation: 3DDAC", Journal of the SID, 4/4, pp. 255-262, 1996).
However, the above described line of gaze following type hologram display method has been associated with the following problem. Namely, in the conventional method for displaying projected images, an area of a region to be displayed at high resolution on the screen is nearly constant as long as a distance between eyes and the display screen is constant. For this reason, an amount of calculations required for the display target image production can also be considered nearly constant. In this case, as shown in FIG. 1, an observer 13 can observe a space 11 through a hologram plane (projection plane) 12, and the gazing target objects in this space 11 are located within a view volume 14 (a gazing target space on the line of gaze). In the conventional method, it has been sufficient to produce projected images of objects in this view volume 14 only within a gazed region 15 (an intersection region between the view volume 14 and the hologram plane 12).
However, in a case of the holography, an image of a single target object is not produced at a particular region on the hologram plane alone but rather the image is produced by synthesizing diffracted lights from the hologram plane, so that there is a need to calculate wavefronts from that target object over the entire hologram plane. In other words, even when the calculation target objects are limited to those objects within the view volume centered around the line of gaze, a region for calculating interference fringes as the hologram is still the entire hologram plane, and a significant reduction in an amount of calculations cannot be realized.
Also, even when the targets are limited to the view volume within the display space, there can be cases where many target objects exist within that view volume depending on a direction of the line of gaze, so that a reduction in an amount of calculations is limited in this regard.
On the other hand, means for displaying computer generated holograms include a display device using acoustic elements (see S. A. Benton, "Experiments in Holographic Video Imaging", 3D Forum, Vol. 5, No. 2, pp. 36-56, 1991, for example) and a display device using liquid crystals (see T. Sonehara, et al., "Moving 3D-CGH Reconstruction Using a Liquid Crystal Spatial Wavefront Modulator", JAPAN DISPLAY '92, pp. 315-318, 1992, for example), and they are expected to be capable of displaying video images.
However, an area that can be displayed by any of these display devices Is extremely small so that a hologram displayed on it is usually viewed by a single eye or in enlargement using lenses. But the use of a larger screen is indispensable in order to increase the realistic sense, and it is physically difficult to realize a larger screen by using a display device according to any of these conventional means so that conventionally the use of a larger screen has been realized by arranging a plurality of display devices.
Moreover, in the holography, in order to display interference fringes as the hologram, the required resolution is much higher than that used in the conventional display device such as TV. In the conventional display device, a pixel width Is at most several tens of .mu.m, but in the hologram display, a display device with a pixel pitch below sub-micron order is required ideally. Consequently, in order to display the hologram by using a screen of the same size, a required resolution will be as high as several tens of thousand times higher. In other words, the hologram production can be considered equivalent to the production of an image in an enormous area. Thus a required amount of calculations for the display image production is enormous in the holography and even in a case of using a provision for arranging a plurality of display devices, an amount of calculations required for computer generated holograms has been the major problem.
In particular, in the holographic video production, there is a need to product a plurality of Interference fringes at high speed so that the suppression of an increase in an amount of calculations is even more serious problem than a case of using a larger screen. As a method for calculating interference fringes at high speed by reducing a required amount of calculations, there is a proposition for re-calculating only moved portions, but even in this method, a required amount of calculations increases as a number of display objects increases and when an area of the display screen is increased, so that there still remains the problem that the holographic video display becomes difficult in such cases.
As described, in the conventional hologram display technique, there is a problem regarding an enormous amount of calculations required by the use of a larger screen and the video display, and this problem largely stems from the nature of the holography. Namely, the holography records interferences of wavefronts of lights emitted by an object in all directions as well as their interferences with a wavefront of the reference light, and lights from the object are propagated in all directions, so that even in a case of calculating the interference fringes for the hologram of only a point object, it is necessary to calculate the wavefronts of lights over the entire hologram plane. Therefore, a required amount of calculations is naturally increased in proportion to an increase in the hologram display area.